:4. In the Department of Natural Sciences, 14 faculty members have a PhD, and 30 faculty members do not have a PhD. In the Department, the number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD. If a third of the male faculty in the Department have a PhD, then what is the number of female faculty in the Department with a PhD?
Answers
Answer:
The number of female faculty in the Department with a PhD is 8.
Step-by-step explanation:
There are 14 + 30 = 44 faculty members.
Of those, x are male and y are female.
Then
x + y = 44.
The number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD.
y = z + w
z is the number of females with PhD.
w is the number of females without PhD.
w = z + 10
If a third of the male faculty in the Department have a PhD
\(\frac{x}{3} + z = 14\)
Now, we can write all variables as functions of z, which is the number of female faculty in the Department with PhD.
The objective is:
To find z from the first equation, that is:
\(x + y = 44\)
To do this, we have to write x and y as functions of z.
Writing x and y as functions z.
\(\frac{x}{3} + z = 14\)
\(\frac{x}{3} = 14 - x\)
\(x = 3(14 - z)\)
\(x = 42 - 3z\)
And
\(y = z + w\)
In which
\(w = 10 + z\)
So
\(y = z + 10 + z\)
\(y = 2z + 10\)
Replacing:
\(x + y = 44\)
\(42 - 3z + 2z + 10 = 44\)
\(-z + 52 = 44\)
\(z = 52 - 44\)
\(z = 8\)
The number of female faculty in the Department with a PhD is 8.
Related Questions
an airplane flew for one hour and landed 100 miles north and 80 miles east from its origin. what was the distance traveled, speed and angle of direction from its origin?
Answers
The distance traveled by airplane is 180 miles.
The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°
The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.
Then, the total distance traveled by airplane will be:
= 100 miles + 80 miles = 180 miles.
The speed can be defined as the distance traveled by the total time taken.
Speed = distance/time
Speed = 180 miles/ 1 hour
Speed = 180 miles/60 minutes
Speed = 3 miles per minute
The angle of direction from its origin will be:
tan (x) = 100 miles/80 miles
x = tan⁻¹ ( 100/80)
x = tan⁻¹ ( 10/8) = tan⁻¹ ( 5/4)
x = 51.34°
Learn more about speed here:
brainly.com/question/13943409
#SPJ1
Mikael has a loan of $40 000.
He pays 1.6% simple interest for six months
How much interest does he pay altogether?
Answers
Step-by-step explanation:
Based on the given conditions,
\( formulate: 1.6\% \times 40000 \times 12 \div 12
\( formulate: 1.6\% \times 40000 \times 12 \div 12Reduce the fraction: \dfrac{2 \times 40000}{125}
\( formulate: 1.6\% \times 40000 \times 12 \div 12Reduce the fraction: \dfrac{2 \times 40000}{125}\)
\(Reduce the fraction: 2 \times320
\(Reduce the fraction: 2 \times320Calculate the product orquotient: 640[tex]
Answer 640
Answer:
\(\sf\longmapsto \: 640\)
Step-by-step explanation:
Based on given cases:
\( \sf \: Formulate: 1.6\% \times 40000 \times 12 \div 12\)
Reduce the fraction:
\( \sf \longmapsto \: \dfrac{2 \times 40000}{125}\)
\( \sf \longmapsto \: 320 \times 2\)
Calculate the product/quotient:
\( \sf\longmapsto \: 640\)
Identify the variable expression that is not a
polynomial.
Answers
Explanation: It’s the only whole number and a polynomial can not be a whole number but must be an expression.
the school lisa goes to is selling tickets to the annual talent show. on the first day of ticket sales the school sold 4 senior citizen tickets and 5 student tickets for a total of $102. the school took in $126 on the second day by selling 7 senior citizen tickets and 5 student tickets. what is the price of on senior citizen ticket and one student ticket?
Answers
Answer: one senior ticket is $8 and one student ticket is $14
Hope this helps a little
pls pls help i'll give u a cookie
A study of 1000 randomly selected flights of a major airline showed that 820 of the flights arrived on time. What is the probability of a randomly selected flight not arriving on time?
a. 50/1
b. 9/50
c. 41/50
d. 1/4
Answers
Answer:
b. 9/50
Step-by-step explanation:
•the probability of the selected flight arriving on time: 820/1000 = 0.82
•find the probability of the flights not being selected by subtracting 0.82 from 1.00: 1.00-0.82=0.18
•now you look for the answer that equals to 0.18
50/1 =50 nope
9/50 =0.18 yes
41/50 =0.82 nope
1/4 = 0.25 nope
9 is 50% of what number?
9 is 25% of what number?
9 is 10% of what number?
9 is 75% of what number?
9 is 150% of what number?
Answers
2) 36
3) 10
4) 12
5) 6
Answer: The answer to this math question are given the following answers to this math question about finding the percent of a number with the given number and a percentage of a number, so anyway, here are 5 following answers:
1). 18
2). 36
3). 10
4). 12
5). 6
Step-by-step explanation: I'm sorry about that, but I don't have any step-by-step explanation for the math question about finding the percent of a number with the given number and a percentage of a number, so anyways, I hope that my short given answer without the step-by-step explanation is very helpful to your own math question about finding the percent of a number with the given number and a percentage of a number, please mark me as Brainliest, take care, always be safe, and have a great rest of the day and good night! :D
Sincerely,
Jason Ta,
The Ambitious of The Brainly And The Role of The TDSB And WHCI Student of The High School.
Real-life Problems Question 6
Answers
The amount of money that Theresa has left is equal to £2,740.
How to write a linear equation to model this situation?In order to write a linear equation to describe this situation, we would assign variables to the cost of flights for each of them and the cost of accommodation for each of them respectively, and then translate the word problem into a linear equation as follows:
Let the variable a represent cost of flights for each of them.
Let the variable f represent cost of accommodation for each of them.
Since Theresa paid for herself and 11 friends to go on holiday with a flight cost of £339 and accommodation cost of £266, a linear equation to describe this situation is given by;
y = 12(a + b)
y = 12(266 + 339)
y = £7,260
For the amount of money left, we have:
Amount of money left = £10,000 - £7,260
Amount of money left = £2,740.
Read more on equation here: brainly.com/question/18912929
#SPJ1
for a standard normal distribution, find:
p(-2.41 < z < -2.2)
round your answer to 4 decimal places.
Answers
Rounding to four decimal places, we have:
P(-2.41 < Z < -2.2) ≈ 0.0061
Using a standard normal distribution table or a calculator, we can find the area under the curve of the standard normal distribution between -2.41 and -2.2.
P(-2.41 < Z < -2.2) = P(Z < -2.2) - P(Z < -2.41)
From a standard normal distribution table, the probability of Z being less than -2.2 is 0.0139 and the probability of Z being less than -2.41 is 0.0078. So,
P(-2.41 < Z < -2.2) = 0.0139 - 0.0078 = 0.0061
Rounding to four decimal places, we have:
P(-2.41 < Z < -2.2) ≈ 0.0061
A normally distributed random variable with a mean of 0 and a standard deviation of 1 is referred to as a standard normal random variable. The letter Z will always stand in for it.
Learn more about standard normal distribution here :
brainly.com/question/17184861
#SPJ4
A researcher conducted a number of descriptive statistics for two variables X and Y. They were as follows: SP = 15; SSx = 3; My = 4; Mx = 2 What is the regression equation for this data? Using this regression equation, what is the value of predicted Y when X
Answers
The regression equation for this data is y = -6+5x.
Using this regression equation, the value of predicted Y when X=3 is 9.
In the given question, a researcher conducted a number of descriptive statistics for two variables X and Y.
We have to find the regression equation for this data.
Then using this regression equation, we have to find the value of predicted Y when X=3.
We have given that
SP = 15
SSx = 3
My = 4
Mx = 2
B1 = Sp / SSx
B1 = 15/3=5
B0 = My-^B1Mx
B0 = 4-5*2=-6
So, the regression equation for this data is:
y = -6+5x
For x=3, the predicted value of y is
y = -6+5*3
y(predict) = 9
To learn more about regression equation link is here
brainly.com/question/14184702
#SPJ4
The write question is given below:
Which algebraic property is used to rewrite 2(x + 3) as 2x + 6? (1 point)
Answers
Answer:
The distributive property
Step-by-step explanation:
2 is being used to multiply both terms (x and 3)
Hope this helps!
Answer:
Distributive property
Step-by-step explanation:
Distributive property: a*(b + c) =(a*b) + (a*c)
2(x + 3) =2*x + 2*3
=2x + 6
The area of the smaller regular pentagon is about 27.5 cm².
What is the best approximation for the area of the larger regular pentagon?
11cm²
172 cm²
70 cm²
275 cm²
Answers
Answer:172 cm²
Step-by-step explanation:
when we use the formula, and we can solve out is like 172.05 and round to tenth and will have the answer
Formula is 1/2 × p × a
$6,000 dollars is invested in two different accounts earning 3% and 5% interest. at the end of one year, the two accounts earned $220 in interest. how much money was invested at 3%
Answers
The amount of money is 4000 was invested at 3%.
Let x be the amount of money invested at 3%.
Then, the amount of money invested at 5% is 6000 - x.
The interest earned on the amount invested at 3% is 0.03x.
The interest earned on the amount invested at 5% is 0.05(6000 - x) = 300 - 0.05x.
The total interest earned is given as $220.
So, we can write the equation:
0.03x + (300 - 0.05x) = 220
Simplifying and solving for x, we get:
0.03x + 300 - 0.05x = 220
-0.02x + 300 = 220
-0.02x = -80
x = 4000
Therefore, $4000 was invested at 3%.
To know more about investment follow
https://brainly.com/question/1529024
#SPJ1
Solve the following inequality:
r/2+15>45
Answers
Answer: r > 30
Step-by-step explanation:
Draw the graphs of the lines below on the same grid to find the coordinates of the point of intersection.
y=3x−3 y=7−2x
Answers
The coordinates of the point of intersection of y=3x−3 and y=7−2x is (2, 3)
Graphing linear equationsFrom the question, we are to graph the given equations.
The graph of the equations is attached below.
In the graph, we can observe that the coordinates of the point of intersection of the is (2, 3)
Hence, the coordinates of the point of intersection of y=3x−3 and y=7−2x is (2, 3)
Learn more on Graphing linear equations here: https://brainly.com/question/21140690
#SPJ1
Find the present value of an annuity which pays ` 200 at the end of each 3 months for 10 years assuming
money to be worth 5% converted quarterly?
(a) ` 3473.86
(b) ` 3108.60
(c) ` 6265.38
(d) None of thes
Answers
The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.
To find the present value of an annuity, we can use the formula:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.
In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.
Plugging in these values into the formula, we get:
PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05
Simplifying the equation, we find:
PV ≈ 200 * (1 - 0.12198) / 0.05
PV ≈ 200 * 0.87802 / 0.05
PV ≈ 35160.4 / 0.05
PV ≈ 7032.08
Therefore, the present value of the annuity is approximately `7032.08.
None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.
For more such questions on annuity
https://brainly.com/question/25792915
#SPJ8
Find the perimeter of a parallelogram whose base is 8cm and another side is 12cm
Answers
A parallelogram
P=2(a+b)
The answer is 64
P=2(a+b)=2·(24+8)=64
Use the information given to identify the ag term of the geometric sequence: a2 = 1/2 r = 2
Answers
Geometric Sequences
A geometric sequence is recognized because each term is calculated as the previous term time a fixed constant called the common ratio (r).
The n-th term can be calculated as:
\(a_n=a_1\cdot r^{n-1}\)Where a1 is the first term and r is the common ratio.
We are not given a1, but we know the value of a2 and r, thus:
\(a_2=r\cdot a_1\)Or, equivalently:
\(a_1=\frac{a_2}{r}\)Calculating:
\(a_1=\frac{\frac{1}{2}}{2}=\frac{1}{4}\)Now calculate a9:
\(\begin{gathered} a_9=a_1\cdot r^8 \\ a_9=\frac{1}{4}\cdot2^8 \end{gathered}\)Calculating:
\(\begin{gathered} a_9=\frac{1}{4}\cdot256 \\ a_9=64 \end{gathered}\)In circle F with m/EFG = 62°, find the angle measure of minor arc EG.
Answers
The angle measure of the minor arc is 62°
What is a circle?A circle is the locus of a point such that its distance from a fixed point (center) is always constant.
The diameter is the length of the line that passes through the center circle touching two points on the circle's circumference.
The arc of a circle is the part or segment of the circumference of a circle.m∠EFG = minor arc EGminor arc EG = 62°
The measure of the arc is 62°
Find out more on circle at: https://brainly.com/question/24375372
#SPJ1
See question in screenshot below.
Answers
The equation of the transformation of the exponential function y = 2ˣ in the form y = A·2ˣ + k, obtained from the simultaneous found using the points on the graph is y = (-2)·2ˣ + 3
What is an exponential equation?An exponential equation is an equation that has exponents that consists of variables.
The given equation is y = 2ˣ
The equation for the transformation is; y = A·2ˣ + k
The points on the graphs are;
(0, 1), (1, -1) and (2, -5)
Plugging the x and y-values to find the value A and k gives the following simultaneous equations;
When x = 0, y = 1, therefore;
1 = A·2⁰ + k = A + k
1 = A + k...(1)
When x = 1, y = -1, which gives;
-1 = A·2¹ + k
-1 = 2·A + k...(2)
Subtracting equation (1) from equation (2) gives;
-1 - 1 = 2·A - A + k - k
-2 = A
1 = A + k, therefore;
1 = -2 + k
k = 2 + 1 = 3
k = 3
Which gives;
y = -2·2ˣ + 3 = 3 - 2·2ˣ
Learn more about the solutions to simultaneous equations here:
https://brainly.com/question/26310043
#SPJ1
Write in words. Use commas and hyphens.
38,492
Answers
Thirty-eight thousand, four hundred and ninety-two
Simply write out the number as you would say it out loud!
Let f(x)=−|x−2|+2 and g(x)=12x−2. Graph the functions in the same coordinate plane. What are the solutions to f(x)=g(x)? Enter your answers in the boxes from smallest to largest.
Answers
Answer: When I took the quiz the answers where-4 and 4
Step-by-step explanation:
I hope this helps.
The graph of the functions f(x) and g(x) on the same coordinates plans is given below.
The solution to f(x) = g(x) is (0.182, 0.182).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Two functions:
f(x) = -|x - 2| + 2
g(x) = 12x - 2
Now,
The graph is given below.
The intersection of the graph of f(x) and g(x) is the solution to f(x) = g(x).
So,
The solution is (0.182, 0.182).
Thus,
The solution is (0.182, 0.182).
The graph is given below.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ2
A summer camp needed
1,148 popsicles. Boxes of
popsicles were sold with
8 in each. How many
boxes did they have to
buy to have enough
popsicles? How many
were left over?
Answers
Answer:
144 boxes, 4 popsicles left over
Step-by-step explanation:
# of boxes and the remainder: 1148/8 = 143 boxes 4 popsicles left over
Since they need to buy full boxes we add 1 to 143 = 144 boxes
A full box is 8 and they only need 4 more so they have 4 left over.
\(8x - 14 = - 2x + 6\)
please give me answer of this question
Answers
Dylan weighs 45 pounds. Use the expression you derived in part I to calculate how much more Bruce weighs than Alan.
Answers
Given: 1) weight of Dylan= 45 pounds
2) weight of Alan= 3 pounds more than twice the weight of Dylan
3)weight of Bruce = 12 pounds less than three times the weight of
Dylan.
To Find: How much more does Bruce weighs than Alan .
Solution:
weight of Dylan= 45 pounds
weight of Alan= 3 pounds more than twice the weight of Dylan
= 3 + ( 2×45) pounds
= (3+ 90) pounds
= 93 pounds
weight of Bruce= 12 pounds less than three times the weight of Dylan
= (3× 45) - 12 pounds
= (135) - 12 pounds
= 123 pounds
therefore, the amount by which Bruce weighs more than Alan will be given by:
weight of Bruce - weight of Alan
= 123 pounds - 93 pounds
= 30 pounds
Hence, Bruce weighs 30 pounds more than Alan.
You flip a coin 100 times and record that 48 are heads and 52 are tails. What is the relative frequency or experimental probability of landing on heads?
whats the percentage
Answers
As a result, the experimental probability of landing on heads is 48%, probability which means that we should expect heads approximately 48 times out of 100 coin flips.
What is probability?Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating an unlikely event and 1 indicating an unavoidable event. Because there are two equally likely outcomes, switching a fair coin and coin flips has a probability of 0.5 or 50%. (Either heads or tails). Probability theory, a branch of mathematics, is concerned with the investigation of random events rather than their properties. It is used in a variety of fields, including statistics, finance, science, and engineering.
The following formula can be used to calculate the relative frequency or experimental probability of landing on heads:
Number of Heads / Total Number of Flips = Experimental Probability of Heads
The number of heads in this case is 48, and the total number of flips is 100. Therefore,
Heads Experimental Probability = 48 / 100 = 0.48
We can multiply this by 100 to get a percentage:
Heads Experimental Probability = 0.48 * 100 = 48%
As a result, the experimental probability of landing on heads is 48%, which means that we should expect heads approximately 48 times out of 100 coin flips.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
A new mixture of self - tanning & moisturizing lotions for everyday use is being developed . This mixture is made by mixing 700 ounces of everyday moisturizing lotion for $0.70 per ounce with self - tanning lotion worth $2 per ounce. If the new self - tanning & moisturizing lotion mixture is to cost $ 1.30 per ounce, how many ounces of the self-tanning lotion should be in the mixture?
The mixture should have ( ) ounces of the self - tanning lotion.
Answers
6 sinθ=5 to the nearest 0.1°
Answers
The value of the equation 6 sinθ=5 for θ is 56.4 degrees
How to evaluate the equationFrom the question, we have the following parameters that can be used in our computation:
6 sinθ=5
Express the equation properly
So, we have the following representation
6 sin(θ) = 5
Divide both sides of the equation by 6
This gives
sin(θ) = 5/6
Evaluate the quotient
sin(θ) = 0.833
Take the arc sin of both sides
θ = sin⁻¹(0.833)
Evaluate
θ = 56.4
Hence, the value of the equation for θ is 56.4 degrees
Read more about trigonometry ratio at
https://brainly.com/question/24349828
#SPJ1
Complete question
Approximate θ in the equation, to the nearest 0.1 degrees
6 sin(θ) = 5
Determine the domain of the graph
Answers
Answer:
Domain: [-11, 8]
Step-by-step explanation:
Domain is the set of x-values that can be inputted into function f(x).
We see from the graph that our x-values span from -11 to 8. Since both are closed dots, they are included in the domain:
[-11, 8] or -11 ≤ x ≤ 8
Precalculus question:
A polynomial f(x) and one or more of its zeros are given. (pictured below)
a) Find all the zeros. Write in the exact simplest form.
b) Factor f(x) as a product of linear factors
c) Solve the equation f(x)=0
Answers
Considering the polynomial f(x) = x^4 - 16x³ + 70x² + 48x - 219, we have that:
a) The zeros are: x = -1.995, x = 1.995, x = 8 - 3i, x = 8 + 3i.
b) The linear factors are: (x + 1.995)(x - 1.995)(x - 8 + 3i)(x - 8 - 3i).
c) The solutions to f(x) = 0 are: x = -1.995, x = 1.995, x = 8 - 3i, x = 8 + 3i.
How to obtain the zeros of the polynomial?The given zero of the polynomial is:
8 + 3i
Hence it's conjugate is also a zero, that is:
8 - 3i.
Thus the first two factors are given as follows:
(x - 8 - 3i)(x - 8 + 3i) = x² - 16x + 64 + 9i² = x² - 16x + 55.
Then the polynomial can be written as follows:
x^4 - 16x³ + 70x² + 48x - 219 = (ax² + bx + c)(x² - 16x + 55).
As a fourth order polynomial can be the product of two second order polynomials. Applying the distributive property to the right side of the equality, we have that:
x^4 - 16x³ + 70x² + 48x - 219 = ax^4 + x³(b - 16a) + x²(55a + c - 16b) + x(55b - 16c) + 55c.
Then the coefficients are given as follows:
a = 1.55c = -219 -> c = -219/55 -> c = -3.98.b - 16a = -16 -> b = 0.Hence the other two factors are given as follows:
x² - 3.98 = 0
x = ± sqrt(3.98)
x = ± 1.995.
The linear factors are:
(x - x')(x - x'')(x - x''')(x - x'''').
In which x', x'', x''' and x'''' are the roots.
The solutions to f(x) = 0 are the roots.
More can be learned about the zeros of a polynomial at https://brainly.com/question/19030198
#SPJ1
What is the simplified form of (3) 4⋅(3) −3
Answers
Answer:
33
Step-by-step explanation:
(3) 4 × (3) - 3
Multiply 3 and 4 to get 12.
12 × 3 - 3
Multiply 12 and 3 to get 36.
36 - 3
Subtract 3 from 36 to get 33.
33
Hope it helps and have an amazing day! =D
~sunshine~